Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ SD32 |
143 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,c^b=cd,d^b=de,g^f=gh61 conjugacy classes — view the full character table.
| maximal subgroup of | #13139283, #13139284, #13139285, … |
| maximal normal subgroup of | #13139283, #13139284, #13139285, … |
| maximal quotient of | #13135811, #13135812, #13135958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 536);